As part of a program to determine the mass distribution of cD galaxy clusters with cooling flows, we obtained a ROSAT image of the cluster A 496. The image reveals sharply peaked emission centered on the cD galaxy. Both the peaked cooling flow emission and the more extended emission filling the cluster are centered on the cD galaxy to within 15 sec . The surface brightness profile is consistent with previous Einstein observations. We measure spatially resolved spectra for the X-ray emission, and find a significant decline in temperature in the innermost 2 min to 4 min. We also find a gradient in absorption due to cold neutral gas, with an excess above the neutral hydrogen column due to our own galaxy in the inner 4 min. The excess absorption, however, is far below previously reported values. The surface brightness profile and the spatially resolved temperature profile are indicative of a cooling flow in the cluster. Cooling flow models fit to the X-ray spectra in the innermost 2 min yield a mass flow rate of 59 solar mass yr(exp -1). The spatially resolved temperature and surface brightness profiles are used to derive the mass distribution of the cluster both in the hot, X-ray emitting plasma and in the unseen dark matter that binds the cluster. To a radius of 1.0 Mpc we find a total cluster mass of 3.44 x 10(exp 14) solar mass ; the X-ray emitting gas mass of 0.75 x 10(exp 14) solar mass to this radius comprises 16 percent of the total cluster mass.